I need to find magnitudes of forces

[Ryuk1990]

Homework Statement

I got a resultant force 28 degrees to the right of the positive y axis. The resultant value is 4200 N. There is one force 45 degrees to the right of the resultant force. The second force is 20 degrees to the left of the positive y axis. All I want to know is how I'm supposed to set up the equations so that I can solve for the two force components.

The Attempt at a Solution

I started out by calculating that there is 17 degrees between the positive x-axis and the first force component.

Is this how I'm supposed to set up the equations?

Force X: F₁*cos17^o + 4200*sin28^o - F₂*cos20^o = 0

Force Y: F₁*sin17^o + 4200*cos28^o + F₂*cos20^o = 0

 

[rl.bhat]

You are right.

 

[Ryuk1990]

Ok, just one more thing. Can you explain to me the theory behind this? I don't get why I have to set X and Y forces to 0.

If I plug in 0 and 0 for the resultant formula which is R = $$\sqrt{FX^2 + FY^2}$$, that doesn't equal 4200 which is what the resultant force is. This confuses me.